Tear off a small piece of paper and answer the question below. When you are done place the paper in the basket and then take out your homework, notebook, and pen/pencil.

Bump in the Road

Write down something you foundconfusing from material covered yesterday.

Properties of Dilations

Module 3LP2

Example 1: Dilating a segment

Dilate with a scale factor 𝑟=2 from 𝑂.O is a point off of segment PQ.

Draw rays from point through 𝑂each of the points and . 𝑃 𝑄

Using a compass, measure the distance from O to P.

Repeat the process to locate Q’.

Connect points ′ and ′ to 𝑃 𝑄draw line segment P′Q’.

Hmmmmmm

Notice the dilation produced a line segment and that line segment is parallel to the original.

What would happen if we selected a different location (point E for example) for the center or different points P and Q?The dilation would still produce a segment and that segment would be parallel to the original.

Hmmmmmm

How would the work we did change if the scale factor were instead of ?We would have to find a point ′ so that it is 𝑃3 times the length of , instead of twice 𝑂𝑃the length of 𝑂𝑃. Same for the point ′𝑄 .(Repeat the compass steps again.)

Example 2: Scale factor .

Example 2

With a scale factor =3, 𝑟Is the dilated segment, P′Q’, still parallel to segment PQ?

Yes…think about the angles created by the transversals.

Example 3

What if we moved center O to the line?

The dilations of points and ( ′ and ′) would 𝑃 𝑄 𝑃 𝑄also be on line . .𝐿

What we have shown: a line segment, after a dilation, is still a line segment.

Mathematicians like to say that dilations map line segments to line segments.

Example 4: Working with Scale Factor

Given center O off segment AB with rays drawn from center O, through points and …𝐴 𝐵Dilate the segments OA and OB with a scale factor

Step 1: Use a ruler to measure the length of OA and OB.

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Given: Calculate a scale factor of |𝑂𝐴′|= · 5 = 2.5 cm |𝑂𝐵′|= · 7 = 3.5 cm

Step 2: Calculate

Step 3: Mark off the points on their respective rays and connect ′ to ′.𝐴 𝐵

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3.5

Question

What happened to our segment AB after the dilation?When we connect point 𝐴′ to point 𝐵′, we will have segment A’B’ which is parallel to the segment AB.

And what do we know about parallel lines or parallel line segments?

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3.5

And what do we know about parallel lines or parallel line segments?

corre

spondi

ng angles!

correspondi

ng angles!

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3.5

Properties of Dilations Dilations map segments to segments,

with a certain scale factor (r).

Dilations map angles to angles which have the same degree

Observations The length of the dilated line segment is

the length of the original segment, multiplied by the scale factor.

The measure of an angle remains unchanged after a dilation.